nicknamed The King and The Lawman by supporters, and Denis the Menace by opposing supporters. He is the only Scottish player to have won the Ballon d'Or award, doing so in 1964, and helped his club win the First Division in 1965 and 1967. He missed their European Cup triumph in 1968 through injury.

Law left Manchester United in 1973 to return to Manchester City for a season, and represented Scotland at the 1974 FIFA World Cup. He retired at the start of the 1974–75 season. Law played for Scotland a total of 55 times and jointly holds the Scottish international record goal tally with 30 goals. Law holds a United record for scoring 46 competitive goals in a single season.

Law moved back to Manchester, boarding with the same landlady with whom he had lived during his time as a City player. His first match for United was against West Bromwich Albion on 18 August 1962, and he made an excellent start, scoring after only seven minutes. The match finished in a 2–2 draw. However, United's form had been erratic since the Munich air disaster in 1958, and because of their inconsistency they spent the season fighting relegation. In a league match against Leicester City Law scored a hat trick but United still lost. They found form in the FA Cup though, with Law scoring another hat trick in a 5–0 win against his old club Huddersfield Town, and they went on to reach the final against Leicester City. Leicester were strong favourites, having finished fourth in the league, but Law scored the first goal as United won 3–1 in what turned out to be the only FA Cup final of his career. He also married his wife Diana that season, on 11 December 1962.

An incident took place that season that Law felt had repercussions in later years. In a match against West Brom on 15 December 1962, the referee Gilbert Pullin consistently goaded Law with taunts such as "Oh, you clever so and so, you can't play", and after the match, Law and his manager Matt Busby reported the matter to the Football Association. A disciplinary committee decided that Pullin should be severely censured, but he did not accept their verdict and quit the game. Law later claimed that "in the eyes of some referees, I was a marked man" and blamed the incident for the "staggeringly heavy punishments" that he received later in his career.

Law scored a number of goals early in the 1963–64 season and was selected to play for a Rest of the World side against England at Wembley, scoring their goal in a 2–1 defeat. He later described this as the greatest honour of his career. His season was interrupted by a 28-day suspension for a sending off that he received against Aston Villa. The unusually cold winter forced United to play many of their fixtures in a short time, and their results suffered. Law later blamed this for United's failure to win a trophy in that season. Despite the lack of silverware, Law enjoyed a prolific goalscoring season and finished the campaign with 46 goals in all competitions, still a club record today.

In 1964–65, Law won the Ballon d'Or award, and Manchester United won their first league title since Munich. Law's 28 league goals that season made him the First Division's top scorer.

The following season, Law injured his right knee while playing for Scotland against Poland on 21 October 1965. He had previously had an operation on the same knee while at Huddersfield, and the injury was to trouble him for the rest of his career.

In 1966, Law asked United's manager Matt Busby to give him a pay rise at his next contract renewal, and threatened to leave the club if he did not get one. Busby immediately placed Law on the transfer list, announcing that "no player will hold this club to ransom, no player". When Law went to see him, Busby pulled out a written apology for him to sign, showing it to the press once he had done so. Law later claimed that Busby had used the incident to warn other players not to do the same thing, but had secretly given him the pay rise. Despite all this, Law scored 23 goals in 36 league appearances during 1966–67, helping United win the league title again.

In 1968, United won the European Cup for the first time, but Law's knee injury was causing him serious problems and he missed both the semi-final and the final as a result. He was regularly given cortisone injections to ease the pain, but playing while the knee was still injured was causing long-term damage. He visited a specialist in January 1968 who wrote to United claiming that a previous operation to remove the cartilage from the knee had failed and recommending that a second operation be performed, but Law was not shown the report for several years and had to continue full training.

In 1968–69, United reached the semi-final of the European Cup, playing AC Milan. United lost the first leg in the San Siro 2–0, winning the second leg at Old Trafford 1–0 with a Bobby Charlton goal. Having scored seven times in the 10–2 aggregate first round victory over Waterford United, Law finished as top scorer in the tournament with 9 goals.

​

Wilf McGuinness took over as first team coach at the start of the 1969–70 season. United finished eighth in the league, but Law missed almost all of the season through injury, and in April 1970 he was transfer listed for £60,000. Nobody made a bid for him, so he stayed at United.

After a poor 1970–71 season, United appointed Frank O'Farrell as manager. They made a good start to the 1971–72 season and finished 1971 five points clear at the top of the league, with Law having scored twelve goals. However, results deteriorated and they finished the season in eighth place. Law scored in the first match of the following season, 1972–73, but his knee injury was troubling him again, and he failed to score for the rest of the season. The poor results continued and O'Farrell was sacked.

Law recommended that United replace O'Farrell with Tommy Docherty, whom he knew from his time playing with the Scottish national side. The club followed his recommendation, and things started well, with the team's improved results lifting them into mid-table.